Skip to main content

Full text of "Analytical Mechanics"

See other formats


CHAPTER XIV.
MOTION  OF A PARTICLE IN A CENTRAL FIELD OF FORCE.
216.   Central Field of Force.  A region is called a central field of force when the intensity of the field at every point of the region is directed toward a fixed point.   The fixed point is called the center of the field.   The force which a particle experiences when placed in a central field of force is called a central force.
217.   Equations of Motions.  Consider the motion of a particle which is projected into a central field of force.   It is evident from symmetry that the path will lie in the plane determined by the center of the field and the direction of projection.    The expressions for the radial and transverse components of the acceleration are, according to the results of 90,
,     dV         dd\*
When the center of the field is chosen as the origin the force acts along the radius vector. Therefore the transverse acceleration vanishes. Suppose the force and the acceleration to be functions of the distance of. the particle from the center, then the last two equations become
d ,